An official website of the United States government
This article advances an argument-based approach to presenting validity evidence for a brief assessment of 3rd–5th grade students’ number sense. Improving students’ number sense has been a goal of K-12 mathematics education in the US since the late 1980’s, and several popular instructional practices are hypothesized to meet this need. However, there is limited evidence in the literature that elementary students’ number sense is improving. We worked to develop a brief assessment for 3rd–5th grade students and then conducted a series of studies to collect evidence that students’ scores reflect their number sense. We present the assessment here along with our intended interpretations and ways to use student scores. We then outline our validity argument, organized by four specific claims addressing the connection between student responses on the assessment and their number sense. Researchers and educators can now use the assessment to efficiently measure elementary students’ number sense.
more »
« less
A Validity Argument for a Brief Assessment of Mature Number Sense
This Brief Report presents an example of assessment validation using an argument-based approach. The instrument we developed is a Brief Assessment of Students’ Mature Number Sense, which measures a central goal in mathematics education. We chose to develop this assessment to provide an efficient way to measure the effect of instructional practices designed to improve students’ number sense. Using an argument-based framework, we first identify our proposed interpretations and uses of student scores. We then outline our argument with three claims that provide evidence connecting students’ responses on the assessment with its intended uses. Finally, we highlight why using argument-based validation benefits measure developers as well as the broader mathematics education community.
more »
« less
- Award ID(s):
- 2100214
- PAR ID:
- 10499941
- Publisher / Repository:
- National Council of Teachers of Mathematics
- Date Published:
- Journal Name:
- Journal for Research in Mathematics Education
- Volume:
- 55
- Issue:
- 1
- ISSN:
- 0021-8251
- Page Range / eLocation ID:
- 51 to 67
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Students who exhibit mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly choose effective problem-solving strategies (McIntosh et al., 1997, https://ro.ecu.edu.au/ecuworks/6819). Due to its dispositional nature, mature number sense is typically measured through in-depth interviews or tests of strategy usage. Yet, the lack of an efficient, rigorously developed measure has made it difficult to collect systematic, replicable evidence on students’ mature number sense. To address this, we developed a brief assessment of mature number sense. The present study provides additional convergent evidence of validity for this measure with US students in grades 3-8 (8–14 years old). We compared middle school (N = 40) and upper elementary school (N = 41) scores from the brief assessment with an established, time-intensive measure (Yang, 2019, https://doi.org/10.1007/s10649-018-9874-8) and an in-depth interview of student strategy usage (Markovits & Sowder, 1994, https://doi.org/10.2307/749290). We found strong correlations (r > 0.7) across all three measures, and this held even when controlling for students’ arithmetic scores (pr > 0.6). Researchers and educators can now use the brief assessment to investigate students’ mathematical thinking and advance knowledge of a key aspect of mathematical cognition.more » « less
-
Validity-related issues are a growing topic within the mathematics education community. Until recently, validation has been treated as something to gather when convenient or is rarely reported in ways that conform to current standards for assessment development. This theoretically-focused proceeding adds to a burgeoning theoretical argument that validation should be considered a methodology within mathematics education scholarship. We connect to design-science research, which is a well-established framework within mathematics education. The goal for this proceeding is to foster the conversation about validation using examples and to communicate information about validation in ways that are broadly accessible.more » « less
-
The early development of spatial reasoning skills has been linked to future success in mathematics (Wai, Lubinski, & Benbow, 2009), but research to date has mainly focused on the development of these skills within classroom settings rather than at home. The home environment is often the first place students are exposed to, and develop, early mathematics skills, including spatial reasoning (Blevins-Knabe, 2016; Hart, Ganley, & Purpura, 2016). The purpose of the current study is to develop a survey instrument to better understand Kindergarten through Grade 2 students’ opportunities to learn spatial reasoning skills at home. Using an argument-based approach to validation (Kane, 2013), we collected multiple sources of validity evidence, including expert review of item wording and content and pilot data from 201 parent respondents. This manuscript outlines the interpretation/use argument that guides our validation study and presents evidence collected to evaluate the scoring inferences for using the survey to measure students’ opportunities to learn spatial reasoning skills at home.more » « less
-
Kombe, Dennis; Wheeler, Ann (Ed.)The purpose of this proceeding is to share a component to a validity argument for a new, computer adaptive mathematics Problem-Solving Measure that is designed for grades six through eight (PSM 6-8). The PSM is a single test, which uses computer adaptive features to measure students’ performance using instructional standards. It is intended to measure students’ problem-solving performance related to instructional standards.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.5951/jresematheduc-2022-0071
